Monojet Signatures from Heavy Colored Particles: Future Collider Sensitivities and Theoretical Uncertainties

In models with colored particle $\mathcal{Q}$ that can decay into a dark matter candidate $X$, the relevant collider process $pp\to \mathcal{Q}\bar{\mathcal{Q}}\rightarrow X\bar{X}+$jets gives rise to events with significant transverse momentum imbalance. When the masses of $\mathcal{Q}$ and $X$ are very close, the relevant signature becomes monojet-like, and Large Hadron Collider (LHC) search limits become much less constraining. In this paper, we study the current and anticipated experimental sensitivity to such particles at the High-Luminosity LHC at $\sqrt{s}=14\,\mathrm{TeV}$ with $\mathcal{L}=3\,\mathrm{ab}^{-1}$ of data and the proposed High-Energy LHC at $\sqrt{s}=27\,\mathrm{TeV}$ with $\mathcal{L}=15\,\mathrm{ab}^{-1}$ of data. We estimate the reach for various Lorentz and QCD color representations of $\mathcal{Q}$. Identifying the nature of $\mathcal{Q}$ is very important to understanding the physics behind the monojet signature. Therefore, we also study the dependence of the observables built from the $pp\to\mathcal{Q}\bar{\mathcal{Q}} + j$ process on $\mathcal{Q}$ itself. Using the state-of-the-art Monte Carlo suites MadGraph5_aMC@NLO+Pythia8 and Sherpa, we find that when these observables are calculated at NLO in QCD with parton shower matching and multijet merging, the residual theoretical uncertainties are comparable to differences observed when varying the quantum numbers of $\mathcal{Q}$ itself. We find, however, that the precision achievable with NNLO calculations, where available, can resolve this dilemma.